Consider a linear AC Thevenin equivalent circuit connected to a load impedance.

The load connected draws the current, and the circuit delivers the power to the load. The alternating current flowing through the load is determined using the rectangular form of voltages, currents, network impedance, and load impedance. The average power delivered to the load is obtained from the product of the square of current and load resistance.

The maximum power transfer delivered to the load is determined by calculating the power derivative with respect to the load resistance. The derivative is then equated to zero for the maximum condition. So, for maximum average power transfer, the load impedance's reactance is the negative of the Thevenin impedance's reactance, and its resistance equals the Thevenin impedance's resistance. When these conditions are met, the load impedance is said to be the complex conjugate of the circuit's Thevenin impedance. The maximum power is obtained when the load impedance meets the above mentioned condition.

According to the maximum average power theorem, the load impedance equals the complex conjugate of the Thevenin impedance. For purely resistive loads, maximum average power transfer occurs when the load impedance equals the magnitude of Thevenin impedance.

In wireless communications, the antenna's impedance is matched to the transmission line or receiver circuit's impedance, maximizing power transfer, ensuring optimal signal strength and enhancing communication quality and range.